What Do CFTs Tell Us About Anti-de Sitter Spacetimes?
Vijay Balasubramanian, Steven B. Giddings, Albion Lawrence
TL;DR
The paper investigates how AdS/CFT data encode bulk spacetime physics, focusing on scattering and transition amplitudes. It develops a bubble-in-AdS picture to map CFT correlators to an S-matrix, and shows that global AdS obstructs standard LSZ due to geodesic periodicity, prompting a patch-based construction into PAdS sectors to define transitions. A large-N collective field theory is proposed to capture local, perturbative supergravity and to relate bulk locality to finite-N effects, highlighting how multi-particle bulk content requires composite boundary operators. The work delineates limitations of reconstructing bulk from boundary data at finite N, clarifies the role of Lehmann representations, and provides a framework for connecting boundary correlators to bulk S-matrices and flat-space scattering in appropriate limits.
Abstract
The AdS/CFT conjecture relates quantum gravity on Anti-de Sitter (AdS) space to a conformal field theory (CFT) defined on the spacetime boundary. We interpret the CFT in terms of natural analogues of the bulk S-matrix. Our first approach finds the bulk S-matrix as a limit of scattering from an AdS bubble immersed in a space admitting asymptotic states. Next, we show how the periodicity of geodesics obstructs a standard LSZ prescription for scattering within global AdS. To avoid this subtlety we partition global AdS into patches within which CFT correlators reconstruct transition amplitudes of AdS states. Finally, we use the AdS/CFT duality to propose a large N collective field theory that describes local, perturbative supergravity. Failure of locality in quantum gravity should be related to the difference between the collective 1/N expansion and genuine finite N dynamics.